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Imagine-self perspective-taking promotes Nash choices in a
simple experimental normal-form game
 Stotland (1969) distinguished two different forms of perspective taking: (1)
imagine-self and (2) imagine-other.
 Imagine-self perspective means imagining what one’s own thoughts and
emotions would be if one were in the situation of the other person
 Imagine-other perspective translates in turn to imagining the thoughts and
emotions of the other person
 Both forms of imagining lead to increased emotional arousal in comparison to
adopting cool, objective perspective
 Imagine-self produces both self-oriented and other-oriented (empathic) emotions
 Imagine-other produces solely other-oriented empathic concern
 Empathy in economic theory
 The concept of empathy despite its importance in Humean (1739) and Smithian
(1759) philosophical enunciations has never gained a decent foothold in economic
theory
 Recently, Grohn and others (2014) suggested that empathy should be perceived
as a distinct psychological mechanism that affects both belief and utility formation in
strategic decision-making
 Grohn and others (2014) suggested that empathy is a cognitive tool that allows to
produce inferences about other’s beliefs in a strategic context, and so to predict
another player’s choice
 Imagine-other perspective-taking is linked with altruistic behavior (Batson, 2011)
– the famous imagine-other-altruism hypothesis
 The following study links the imagine-self perspective-taking to Nash equilibrium
behavior of decision-makers
 Since Nash equilibrium concept is believed to model self-interested behavior of
decision-makers involved (Cohen, 1998), and the following study links imagine-self
perspective-taking to Nash equilibrium behavior, the imagine-self-self-interest
hypothesis could be considered
 Perhaps empathy-behavior link can be decomposed not only into imagine-otheraltruism hypothesis but also imagine-self-self-interest hypothesis
 We examined subjects’ behavior in a simple experimental normal-form game, in
which one of the two players (row player) can suffer a monetary loss only if (1) she
plays her Nash equilibrium pure strategy and (2) the other player (column player)
plays her dominated pure strategy
 Note the proposed game is solvable through the process of iterative elimination
of the strictly dominated strategies. It is easy to see that the R strategy of a column
player is strictly dominated by the L strategy. Once the R strategy is eliminated the B
strategy of a row player becomes strictly dominated. As a result there is a single
strict pure strategy Nash equilibrium (T, L)
 There were four experimental groups numbering about one hundred participants
each. Each group was given different instructions.
 Participants of the experiment were undergraduate students of Warsaw School of
Economics (SGH). In particular first year and second year students participated in the
experiment. During first year of studies at Warsaw School of Economics students do
not choose any particular profile of studies (in order to complete a bachelor’s degree
third-year students major in one of the taught disciplines, ranging from business and
economics studies, through decision sciences and information systems to political
science and international relations).
 The instructions are constructed in such a way as to test how behavior of a given
player, either row or column, varies as the player is guided to consider choices of an
opponent. As with imagine-self perspective-taking people try to imagine themselves
in other people’s shoes, instructions given to groups 3 and 4 are intended to induce
imagine-self perspectives in subjects belonging to those groups.
Strategy chosen
Number of participants that chose the
Relative frequency of the given choice
given strategy
Group 1
T
39
0.371
B
66
0.629
Group 2
L
94
0.904
R
10
0.096
Group 3
TL
56
0.583
TR
1
0.010
BL
33
0.344
BR
6
0.063
Group 4
TL
36
0.364
TR
3
0.030
BL
58
0.586
BR
2
0.020
 In this study we decided to formulate the following research hypotheses.
Hypothesis 1
In the first experimental group a proportion of subjects choosing a strategy B is
higher than a proportion of subjects choosing a strategy T.
Hypothesis 2
A proportion of subjects choosing T in the third experimental group is higher than a
proportion of subjects choosing B in the third experimental group.
Hypothesis 3
A proportion of subjects choosing T in the third experimental group is higher than a
proportion of subjects choosing T in the first experimental group.
Hypothesis 4
A proportion of subjects choosing L in the third experimental group is higher than a
proportion of subjects choosing R in the third experimental group.
Hypothesis 5
A proportion of subjects choosing TL in the third experimental group is higher than a
proportion of subjects choosing BL in the third experimental group.
 In this study we decided to formulate the following research hypotheses.
Hypothesis 6
A proportion of subjects choosing L in the second experimental group is higher than
a proportion of subjects choosing R in the second experimental group.
Hypothesis 7
A proportion of subjects choosing strategy L in the fourth experimental group is
higher than a proportion of subjects choosing R in the fourth experimental group.
Hypothesis 8
A proportion of subjects choosing L in the fourth experimental group is equal to a
proportion of subjects choosing L in the second experimental group.
Hypothesis 9
A proportion of subjects choosing L in the second experimental group is higher than
a proportion of subjects choosing T in the first experimental group.
Hypothesis number
P-value
Hypothesis
1
0.005409
not rejected
2
0.0411
not rejected
3
0.001263221
not rejected
4
2.2e-16
not rejected
5
0.009593
not rejected
6
2.2e-16
not rejected
7
2.2e-16
not rejected
8
0.2854253
not rejected
9
1.506029e-16
not rejected
We believe that the threat of suffering monetary losses can effectively discourage
the row players from choosing strategy T in the first experimental group. The row
players can rationally take the possibility of playing strategy R by column players into
account.
The column players can play strategy R either because of their not full rationality
(and so the column players may e.g. do not understand the decision problem
completely or make mistakes in solving it or indicating their choices) or their specific
not self-interested motivation.
As already mentioned, the row players may choose non-Nash equilibrium strategy
because of rational expectations that (i) the column player is not fully rational or (ii)
is motivated to act in a not self-interested manner.
The latter can be at least partially explained by social value orientation (SVO) theory
(McClintock, 1972; Griesinger and Livingston, 1973). The row player may know that
the column player can exhibit competitive orientation and so seek for a
maximization of her relative gain. Note that selecting strategy R by the column
player may mean in fact sacrificing risk-free 100 euros to inflict losses on the row
player. The self-interested column decision-maker should instead select strategy L in
order to maximize her individual gain.
The row players may choose non-Nash equilibrium strategy because of rational
expectations that the column player is not fully rational.
In neoclassical economics full rationality means that the ratio of decision maker’s
cognitive capacities to problem complexity always equals 1 (Hendrikse, 2003).
Consequently, a decision maker is able to immediately solve any problem and makes
no mistakes.
The row players may attribute some other form of rationality (other than full
rationality) to column players, i.e. for example bounded (limited) rationality or
procedural rationality (cf. Hendrikse, 2003).
Bounded rationality occurs when the ratio of decision maker’s cognitive capacities to
problem complexity is lower than 1 (Simon, 1961).
Procedural rationality occurs when the ratio of decision maker’s cognitive capacities
to problem complexity is nearly zero (Hendrikse, 2003).
Other than full rationality concepts of rationality allow the possibility of errors made
by the decision-maker.
When we look at the results, we can conclude that in our experimental game the
pure strategy Nash equilibrium concept does not work well. Note that in game
equipped with instructions that do not induce imagine-self perspective, the majority
of outcomes would be (B, L) instead of the single strict pure strategy Nash
equilibrium (T, L).
The pure strategy Nash equilibrium concept works better when assisted with the
experimental instructions intended to induce imagine-self perspective. In game
equipped with such an instruction the majority of outcomes would be (T, L).
It seems that somehow the imagine-self perspective-taking promotes Nash choices
in our simple experimental normal-form game.
One possible explanation can be found on the grounds of psychological distance
theory. Adopting imagine-self perspective by the row player shortens the
psychological distance (Liberman et al., 2007) between her and the column player. In
consequence, the column player may appear to her more similar (similarity is one of
the forms of psychological distance, see Liviatan et al., 2006). If so, “psychologically
closer” individual may seem to decision-maker more likely to be rational, which is
how decision-makers tend to perceive themselves (see e.g. Rawls, 1971; O’Neill,
1998; Hendrikse, 2003; Hollis, 2013). As a result, row player’s confidence that the
opponent will play her dominant strategy may rise and so the number of Nash
choices made by row players in our experiment.
It seems that somehow the imagine-self perspective-taking promotes Nash choices
in our simple experimental normal-form game.
Note that the third (and the fourth) experimental condition could be in fact also
perceived as a game with oneself, i.e. the decision-maker may “impose herself” (e.g.
her own preferences) on the other player. Then the column player in the third
experimental condition may appear to the decision-maker really “psychologically
close” and definitely more predictable comparing to the first condition.
It seems that somehow the imagine-self perspective-taking promotes Nash choices
in our simple experimental normal-form game.
It is also worth noticing that imagine-self perspective taking by participants allows to
receive significantly more game results that would be generated in a society
consisting of (i) sufficiently rational and (ii) self-interested people (pairs of choices –
TL). Perhaps then imagine-self perspective-taking can act as a specific cognitive
device promoting self-interested behavior of society members in strategic
interactions, in the best interest of the whole society. Imagine-self perspective taking
may be then close to this form of Smithian mindreading (1759) that assists working
of the “invisible hand”.